As the engine rotates, the cam chain turns the cam at 50% the speed of the crankshaft. on the left end of the camshaft, there is a smaller cam under a small cover. This cam opens and closes the points. What you're calling the contack breakers should be "contact" breakers, or breaker points. As these points open, breaking contact ( hence the name) the electromagnetic field in the ignition coils collapses, inducing a high voltage into the secondary windings, giving what you call the spark to the spark plug. This ignites the fuel-air mixture in the cylinder, and makes the engine run.
Modern autos and bikes have solid state/transistorized ignitions, but the concept is still the same: when you stop the flow of current to the primary side of the ignition coil, it creates a spark in the secondary side. This spark is applied to the spark plug via the plug wire, or in the case of modern coil-over-plugs, the coil is part of the plug cap, and there is no spark plug wire.
Your points are nothing more than an engine driven mechanical switch. They are supposed to be set in such a way they they open at precisely the correct point to make the plug fire just before the piston reaches the top of the compression stroke. Because they are a mechanical device, the little rubbing block that actuated the points wears. The actual electrical contacts themselves pit over time. That is why they are changed.
If you make the gap wider, the spark happens earlier. If you close the gap, later. That is why you set the gap first. Then you move the point set on its adjustments to get it to open at the right spot. The you do the other one, the right side in this case.
